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Real analysis question

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f:Rnxn-->Rnxn be defined by f(A) = A2. Prove that f is differentiable. Find the derivative of f.

    2. Relevant equations

    f(a + h) = f(a) + f'(a)h + [itex]\phi[/itex](h)

    3. The attempt at a solution

    f(A + H) = (A + H)2 = A2 + AH + HA + H2

    f(A) is given by A2. So the sum of the derivative operator and the remainder term is AH + HA + H2. The problem is that I don't know how to determine which terms are part of the derivative.
  2. jcsd
  3. Sep 28, 2011 #2


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    Staff Emeritus
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    Gold Member

    The derivative is the linear part of AH+HA+H2 in H. So the question is which part is linear and which part is not?
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